Space of modular forms of level 1016, weight 4, and Character 1016.r

• Label: 1016.4.r
• Level: $1016$
• Weight: $4$
• Character orbit: 1016.r
• Rep. character: $\chi_{1016}(353,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $576$
• Sturm bound: $512$

Defining parameters

Level:	\( N \)	\(=\)	\( 1016 = 2^{3} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1016.r (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 127 \)
Character field:			\(\Q(\zeta_{9})\)
Sturm bound:			\(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1016, [\chi])\).

	Total	New	Old
Modular forms	2328	576	1752
Cusp forms	2280	576	1704
Eisenstein series	48	0	48

Trace form

576 * q - 30 * q^5 - 18 * q^7 + 54 * q^13 - 252 * q^15 + 564 * q^21 - 7200 * q^25 + 648 * q^27 + 252 * q^29 - 1548 * q^31 - 504 * q^33 + 390 * q^35 - 630 * q^37 + 102 * q^39 + 666 * q^41 + 342 * q^45 + 516 * q^47 - 1278 * q^49 + 1836 * q^51 + 2160 * q^55 - 252 * q^57 - 1734 * q^59 + 540 * q^61 + 7776 * q^63 + 1044 * q^65 - 2646 * q^67 + 810 * q^69 + 294 * q^71 - 342 * q^75 - 1848 * q^77 + 3780 * q^79 - 1092 * q^81 + 444 * q^83 - 5790 * q^87 - 4194 * q^89 + 246 * q^91 + 3462 * q^93 - 10728 * q^95 + 3852 * q^97 - 3780 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1016, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1016, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1016, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(254, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(508, [\chi])\)\(^{\oplus 2}\)